Problem: The grades on a language midterm at Santa Rita are normally distributed with $\mu = 70$ and $\sigma = 5.5$. Ishaan earned a $72$ on the exam. Find the z-score for Ishaan's exam grade. Round to two decimal places.
A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Ishaan's exam grade by subtracting the mean $(\mu)$ from his grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{72 - {70}}{{5.5}}} $ ${ z \approx 0.36}$ The z-score is $0.36$. In other words, Ishaan's score was $0.36$ standard deviations above the mean.